M. Á. Goberna Torrent
An optimization problem is said to be ill-posed (term introduced by J. Renegar in 1994) when arbitrary small perturbations of the constraints provide consistent (or feasible) as well as inconsistent (or infeasible) problems.
In this talk, we characterize the well-posed linear conic programming problems and provide lower and upper bounds for the distance from a given consistent linear conic programming problem (usually called nominal) to the family of ill-posed linear conic programming problems equipped with the same closed pointed convex cone with non-empty interior and the same objective functional as the nominal one. The lower and upper bounds coincide for certain family of cones which includes the positive cone in finite dimensional Euclidean spaces and the cone of positive semi-definite matrices in the space of symmetric matrices, but not the second order cone.
Palabras clave / Keywords: linear conic programming, well-posedness, ill-posedness
Programado
Sesión GT11-2: Optimización Continua-2 (OPTIMIZACIÓN-2). Organizador: Juan Parra López
29 de mayo de 2018 10:30
Sala 6
